Solving this Rational Equation?

Question

Here's my equation: $\frac{f + 3}{2}$ - $\frac{f - 2}{3}$ = 2

I know that the LCD: 6

Here's how I solved it:

$\frac{f + 3}{2}$$\frac{(3)}{(3)}$ - $\frac{f - 2}{3}$$\frac{(2)}{(2)}$ = $\frac{2}{1}$$\frac{(6)}{(6)}$

= $3f + 9 - 2f - 4 = 12$

= $7$

Text's answer: $-1$

I don't understand what went wrong...

Answer 1

$$3(f+3)-2(f-2)=2(6)$$

$$3(f+3)-2f-2(-2)=2(6)$$

$$3(f+3)-2f\color{blue}+4=2(6)$$

Answer 2

(3f+9)-(2f-4)=12 Remember to separate them by brackets:

We can do one better by adding 12 to the -4. Why??? Well, logically speaking, if we start at 3f+9, we go downwards by 2f-4 to reach twelve. If we want to go downwards by 12 further. We have to make sure the number being subtracted is bigger by 12 numbers.

(3f+9)-(2f+8)=0

Here are the rest of your steps:

3f+9=2f+8
3f+1=2f
f+1=0
f=-1